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A spherical convex body R is called reduced if any convex body properly contained in R has thickness smaller than the thickness Δ (R) of R. We show that for every reduced spherical convex polygon V there exists its boundary point such that the disk of radius Δ (V) centered at this point contains V. [ABSTRACT FROM AUTHOR]

The univalent function ϕ SG (z) : = 2 / (1 + e − z) maps the open unit disk | z | < 1 onto a sigmoid domain | log (w / (2 − w)) | < 1. The sharp radii constants have been computed for the classes involving ratios f / g and g / (z p) of analytic functions f , g and p defined in | z | < 1 such that p is subordinate to ϕ SG , the other two ratios are subordinate to 1 + z , e z or z + 1 + z 2 and the quantity z f ′ / f lies in a certain region of the right half plane. [ABSTRACT FROM AUTHOR]

Canadian astrophysicist Hubert Reeves (April 2011) considers Audouin Dollfus to be one of the greatest contemporary French astronomers. In particular, he discovered Saturn’s satellite Janus, determined the composition of the soil on Mars, detected atmospheric residue on Mercury and helped choose the landing site for the Apollo 11 mission, which enabled Neil Armstrong to set foot on the Moon for the first time. He was also a high-flying aeronaut, as he still holds the world record for the highest manned flight in a balloon equipped with an astronomical telescope.

In this paper, sharp bounds on the Hankel determinant H 3 , 1 (f) : = | a 1 a 2 a 3 a 2 a 3 a 4 a 3 a 4 a 5 | are given for the functions f of the form f (z) = z + a 2 z 2 + ⋯ such that z f ′ (z) / f (z) or 1 + z f ″ (z) / f ′ (z) are subordinated by z + 1 + z 2 . [ABSTRACT FROM AUTHOR]